🧵 Math book recommendation request
Anonymous at Sat, 16 Mar 2024 20:07:36 UTC No. 16081822
Hello /sci/, math undergraduate student here. I was looking into multivariable integration since I have it next semester and all resources I found are very strange. Baby Rudin's ch 10 11 do it very weirdly and very short/terse manner, and I did not like Spivak Calculus on Manifolds either.
I tried reading Munkres Analysis on Manifolds and even he has that portion not as well as he dealt with the multivariable differentiation
Any good suggestions for this topic? Anything is appreciated. I enjoyed Munkres Analysis on Manifolds treatment of differentiation a lot.
Any suggestions?
I need an easy book that lays down all the theory needed in detailed comprehensive manner which i can easily access, maybe some manifold intuition too
Later of course I will solve Rudin and Spivak problems but I need a book to learn
Anonymous at Sat, 16 Mar 2024 20:35:14 UTC No. 16081853
>>16081822
Zorich Vol 2 covers it, I've haven't read that yet, but Vol 1 is my favorite analysis book.
Anonymous at Sun, 17 Mar 2024 00:00:10 UTC No. 16082196
https://www.math.stonybrook.edu/~ak
Anonymous at Sun, 17 Mar 2024 00:50:00 UTC No. 16082249
>>16081822
There really aren't great books at that level on the subject, since you need considerably more background on the subject to understand the motivation behind most of the concepts involved. Volume 1 of Spivak's "A comprehensive introduction to differential geometry" is probably the best book accessible at your level; it's much more readable than his calculus on manifolds book. Bishop and Goldberg's "tensor analysis on manifolds" is shorter and also explains things pretty well.
To get the full picture involving the deRham cohomology there's Bott and Tu's "differential forms in algebraic topology" but it definitely requires that you already know a lot of algebraic topology to make sense of it, so you have a long way to go before then.
Anonymous at Sun, 17 Mar 2024 07:50:19 UTC No. 16082663
>>16082249
How to get into cohomology then?
Anonymous at Sun, 17 Mar 2024 08:11:03 UTC No. 16082677
Are there good series for physicists, engineers or applied mathematicians? Something like "Cambridge Texts in Applied Mathematics", but more organized for progressive learning? I take the first volume, read it, then I take the second volume, read it, etc.
Anonymous at Sun, 17 Mar 2024 08:12:54 UTC No. 16082680
>>16081822
Bogachev
Anonymous at Sun, 17 Mar 2024 19:02:46 UTC No. 16083327
>>16082680
Which book
Anonymous at Sun, 17 Mar 2024 19:07:43 UTC No. 16083338
Read Springer
Anonymous at Sun, 17 Mar 2024 19:07:53 UTC No. 16083339
>>16081822
you sure do seem to like talking about yourself on social media
Anonymous at Sun, 17 Mar 2024 19:28:17 UTC No. 16083370
>>16083338
WHICH SPRINGER BOOK
Anonymous at Mon, 18 Mar 2024 18:27:55 UTC No. 16085092
>>16081822
Spivak's Calculus on Manifolds is great. Wtf is your problem with it?
Pax at Tue, 19 Mar 2024 09:56:31 UTC No. 16086245
>>16083327
Measure theory
Anonymous at Tue, 19 Mar 2024 14:09:51 UTC No. 16086524
>>16085092
Fucking imbecile. It contains many errors including some serious ones in proofs, and it's hand wavy in many places.
Anonymous at Tue, 19 Mar 2024 15:09:27 UTC No. 16086595
>>16083339
kek
Anonymous at Tue, 19 Mar 2024 15:12:32 UTC No. 16086599
>>16081822
hubbard and hubbard
you don't need more
Anonymous at Tue, 19 Mar 2024 18:28:38 UTC No. 16086848
>>16085092
It is the most retarded and most hideous piece of mathematical textbook I have ever seen the fact that this and rudin's chapter 10 and 11 exist and are celebrated as good mathematical texts is a crime in name of mathematics
Anonymous at Tue, 19 Mar 2024 18:30:46 UTC No. 16086850
>>16082663
Just read Hatcher. If that's a problem read a real algebraic topology book like Spanier.
Anonymous at Tue, 19 Mar 2024 19:05:54 UTC No. 16086884
>>16086524
>It contains many errors including some serious ones in proofs, and it's hand wavy in many places
Examples?
> It is the most retarded and most hideous piece of mathematical textbook I
It's very good. I learned a lot from it.
Anonymous at Tue, 19 Mar 2024 19:11:06 UTC No. 16086890
>>16081822
Vector calculus, linear algebra, and differential forms - a unified approach - hubbard
Anonymous at Tue, 19 Mar 2024 19:12:09 UTC No. 16086892
>>16086599
>and a good moring to you, sir
Anonymous at Tue, 19 Mar 2024 20:45:33 UTC No. 16087007
>>16081822
Multivariable analysis from Vector to Manifold - Mikusinski